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HAL Id: hal-00569451 https://hal.archives-ouvertes.fr/hal-00569451 Submitted on 25 Aug 2011 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Vocal tract resonances in singing: Strategies used by sopranos, altos, tenors, and baritones Nathalie Henrich Bernardoni, John Smith, Joe Wolfe To cite this version: Nathalie Henrich Bernardoni, John Smith, Joe Wolfe. Vocal tract resonances in singing: Strategies used by sopranos, altos, tenors, and baritones. Journal of the Acoustical Society of America, Acoustical Society of America, 2011, 129 (2), pp.1024-1035. 10.1121/1.3518766. hal-00569451
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Page 1: Vocal tract resonances in singing: Strategies used by ...

HAL Id: hal-00569451https://hal.archives-ouvertes.fr/hal-00569451

Submitted on 25 Aug 2011

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

Vocal tract resonances in singing: Strategies used bysopranos, altos, tenors, and baritones

Nathalie Henrich Bernardoni, John Smith, Joe Wolfe

To cite this version:Nathalie Henrich Bernardoni, John Smith, Joe Wolfe. Vocal tract resonances in singing: Strategiesused by sopranos, altos, tenors, and baritones. Journal of the Acoustical Society of America, AcousticalSociety of America, 2011, 129 (2), pp.1024-1035. �10.1121/1.3518766�. �hal-00569451�

Page 2: Vocal tract resonances in singing: Strategies used by ...

Vocal tract resonances in singing: Strategies used by sopranos,altos, tenors, and baritones

Nathalie HenrichDepartment of Speech and Cognition, GIPSA-lab (UMR5216: CNRS, INPG, University Stendhal, UJF),Grenoble, France

John Smith and Joe WolfeSchool of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia

(Received 13 July 2010; revised 21 October 2010; accepted 27 October 2010)

The first two vocal tract resonances (R1 and R2) of 22 classically trained sopranos, altos, tenors, and

baritones were measured while they sang four different vowels over their normal pitch range. The

resonances of the tract and the harmonics of the voice were measured simultaneously by injecting a

broadband acoustic current into the tract at their mouth. Sopranos were found to tune R1 close to the

fundamental frequency f0 (R1:f0 tuning) over at least part of their upper range for all vowels studied,

particularly when f0 was around or above the value of R1 for speech. Additionally, most sopranos

employed R2:2f0 tuning over some of their range, often simultaneously with R1:f0 tuning. Altos used

R1:f0 tuning for vowels having lower values of R1 in speech, but can switch to R1:2f0 tuning in the

lower part of their range. Tenors and baritones generally used R1:2f0 and R1:3f0 tunings over part of

their range and employed a number of different tunings to higher harmonics at lower pitch. These

results indicate that singers can repeatedly tune their resonances with precision, and that there can be

considerable differences in the resonance strategies used by individual singers, particularly for

voices in the lower ranges. VC 2011 Acoustical Society of America. [DOI: 10.1121/1.3518766]

PACS number(s): 43.75.Rs [ADP] Pages: 1024–1035

I. INTRODUCTION

The frequencies of the first two or three resonances of

the vocal tract may be varied by movements of articulators,

such as tongue, jaw, lips, and larynx. Each resonance, with

frequency R1, R2, etc., usually produces a maximum in the

envelope of the spectrum of the voice. In speech, these spec-

tral maxima1 have roles in characterizing vowels and some

consonants (Fant, 1970; Stevens, 2000; Clark et al., 2007).

The vocal tract resonances not only continue to perform these

functions when singing text, but can also have important

additional functions. These resonances can enhance the over-

all sound level of the voice by improving the coupling

between the glottis and the external radiation field. The

vibrating vocal folds produce a signal with fundamental fre-

quency f0, which is usually unrelated to the Ri. When a har-

monic of the voice (an integral multiple of f0) lies sufficiently

close to any one of the Ri, that harmonic is radiated strongly.

Further, it has been suggested that if f0 occurs at a frequency

slightly below that of a resonance, the inertive load on the

vocal folds may enhance their vibration and stability (Titze,

1988, 2008). Maintaining a high sound level is important to

many classical singers, who often perform unamplified in

large auditoria, sometimes accompanied by large orchestras.

Resonance tuning, i.e., the adjustment of the frequency of a

resonance to match that of a harmonic of the voice, thus

offers singers a technique that is believed to increase loudness

with little extra vocal effort. These adjustments also have

implications for speech and singing synthesis. This paper

investigates whether singers in different vocal ranges tune

R1 and/or R2 to the fundamental and/or other harmonics of

the voice.

The possibility of implementing resonance tuning nec-

essarily requires a suitable overlap in frequency between the

possible range of a resonance and a harmonic of the voice.

Figure 1 illustrates various possible tuning strategies, includ-

ing those that have been measured and/or proposed in the lit-

erature for four voice types: Soprano, alto, tenor, and bass.

The significant differences in possible strategies between

these vocal ranges are now discussed.

A. Soprano and alto ranges

Figure 1(a) illustrates that the nominal range of the soprano

voice, about C4 to C6, (261–1046 Hz) roughly coincides with

the range of R1 in speech. This raises the possibility that sopra-

nos might tune R1 to the fundamental frequency f0, as con-

cluded by Sundberg et al. (Sundberg, 1975, 1987; Sundberg and

Skoog, 1997). Later studies confirmed that classically trained

sopranos do indeed raise R1 during singing over the higher part

of their range (500 < f0 < 1000 Hz), so that it is approximately

the same as f0 (Joliveau et al., 2004a). This R1:f0 tuning is per-

haps more likely in the upper octave of the soprano range, when

f0 starts to increase above the values of R1 in speech.

There exist some additional possibilities for the soprano

voice. Figure 1(a) indicates that R2:2f0 tuning could occur in

the upper octave of the soprano range from C5 to C6. R1:2f0tuning might also occur in the lower octave of the soprano

voice (C4 to C5). Interestingly for coloratura or other sopranos

who sing well above the normal range and past the upper limit

of R1, there is only one possible strategy, i.e., to use R2:f0 tun-

ing. Recent measurements have confirmed that this strategy is

indeed employed (Garnier et al., 2010). That very high

range—out of reach of most sopranos—is not studied here.

1024 J. Acoust. Soc. Am. 129 (2), February 2011 0001-4966/2011/129(2)/1024/12/$30.00 VC 2011 Acoustical Society of America

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The nominal range of the alto voice (G3 to G5) has con-

siderable overlap with the soprano range and altos might

also be expected to utilize similar tuning strategies, e.g.,

R1:f0 tuning might be expected, particularly over the higher

part of their range. Figure 1(b) shows that R1:2f0 tuning is

also a possible strategy, particularly in the lower range.

Indeed it has been proposed that R1:2f0 tuning is employed

in the “belting” style of singing (Schutte and Miller, 1993).

More recently R1:2f0 tuning over the range 300 < f0 < 500

has been found in a traditional Bulgarian style of singing,

which produces a voice of unusual timbre and surprising

loudness (Henrich et al., 2007). The possibility of R2:2f0tuning, or perhaps even R2:3f0 tuning, exists in the upper

region of the alto range.

B. Tenor, baritone, and bass ranges

The lower fundamental frequency of the male voice range

offers a much wider range of strategies. In the lowest range of

men’s voices ( f0 � 100 Hz), systematic resonance tuning would

seem to offer little advantage; the harmonics are closely spaced

and at least one will usually fall sufficiently close to any normal

value of R1 to obtain some useful boost in sound level. Indeed

Fig. 1(d) indicates that six or seven harmonics fall within the nor-

mal range of R1 in the lower octave—one is likely to be a useful

match for any note–pitch combination, with little adjustment.

The values of R1 might then be similar to those of speech,

although small shifts in resonances might still be advantageous

to enhance further the sound level. Similarly there are also many

possibilities for matching R2 with harmonics in this region.

For baritones and tenors, however, deliberate tuning

might have advantages. Near the upper end of the tenor range

(nominally about C5 at 523 Hz), the harmonic spacing

approaches 500 Hz and consequently it is then possible that

no harmonic might be nearer than 250 Hz to the value of R1

for a vowel in speech. For the vowel /u/, the typical values of

R1 are low and fall well within the normal singing f0 range of

baritones, and so, for this vowel especially, one might expect

some baritones and tenors to take advantage of R1:f0 tuning.

Figure 1(c) shows that R1:2f0 tuning is also possible over the

full tenor range, and that R1:3f0 tuning might be useful in the

lower part of the range. There are also several possibilities of

tuning R2, including R2:2f0, R2:3f0, and R2:4f0 tuning.

Strong evidence for R1:f0 tuning in tenors is not avail-

able. Titze et al. (1994) used an analysis-by-synthesis tech-

nique and adjusted both formant frequencies and glottal

parameters of a linear source-filter model to match the spec-

tra of a sample of tenor voices. The frequency of the first res-

onance was found well above the fundamental for all vowels

except /u/. They interpreted the absence of tuning R1 to f0 in

tenor voices as due to a desire to maintain a characteristic

male quality. Later Tom and Titze (2001), also using synthe-

sis, reported that the tenor in that study appeared to tune R1

to f0 in two out of nine possibilities for the vowel /a/.

However, there is indirect evidence for all the other possi-

ble resonance tunings discussed above for the male voice. Thus

Miller and Schutte (1990) reported evidence for R1:2f0 and

R2:2f0 tuning on isolated notes of baritones via measurements

of sub- and supra-glottal pressure. There is also evidence

FIG. 1. A schematic showing possible resonance-tuning strategies for dif-

ferent voice ranges on a log–log plot. Typical ranges of the vocal tract

resonances R1 and R2 are shown in gray. Within each voice range the diago-

nal, dashed gray lines indicate when a resonance frequency coincides with

the nth harmonic (nf0) of the sung pitch ( f0); i.e., the possible relationships

Ri ¼ nf0 for n ¼ 1–8. Only the first eight harmonics are shown. The vertical

dashed lines indicate the nominal limits of each singing range. Within the

soprano, alto, and tenor ranges, the double-headed diagonal arrows indicate

various possible tuning strategies, including those that have been measured

or proposed. Gray double-headed arrows indicate some of the possibilities

for the bass range. A known tuning (R2:f0) is also shown for the coloratura

or whistle range that lies above the normal soprano range studied in this

paper (Garnier et al., 2010).

J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types 1025

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suggesting R1:2f0 tuning for males in the ojkanje style of Cro-

atian singing (Boersma and Kovacic, 2006). Schutte et al.(2005) suggested that R2:3f0 tuning occurs on the high Bb4

notes on recordings of tenor(s). Neumann et al. (2005) inferred

from the sound spectrum that, for male opera singers in the

“chest” register, the second harmonic was “resonated by” the

first resonance (R1:2f0 tuning) and the fourth harmonic by R2

(R2:4f0 tuning) with the implication that then R2� 2R1� 4 f0.Across the passaggio, R2 often fell near 3f0.

To investigate resonance tuning reliably, it is important

that the frequencies of the resonance and the relevant harmonic

should be determined precisely and independently (Joliveau

et al., 2004a). For example, studies of singing at high pitch

that use only the sound and determine the resonance frequen-

cies from the voice harmonics are inherently quite inaccurate

(Monsen and Engebretson, 1983) and are further complicated

by the frequency dependence of the glottal source.

Because most previous studies used indirect or impre-

cise methods to deduce or to estimate resonance frequencies,

this paper takes a different approach that involves injecting a

synthetic broadband acoustic signal at the singer’s mouth

during singing. A microphone records both the singing and

the response of the vocal tract to this broadband excitation.

For this study, only singers trained in the classical tradition

were investigated; they were volunteers with experience

ranging from amateur to professional.

II. MATERIALS AND METHODS

A. Resonance measurements

The measurements were conducted at UNSW in a room

treated to reduce reverberation and to reduce external noise.

The technique used for resonance measurement has been

described previously (Epps et al., 1997; Joliveau et al., 2004b).

Briefly, a small source of broadband acoustic current and a

microphone are positioned adjacent to each other on a flexible

mounting so that they just touch the subject’s lower lip through-

out the experiment. This does not affect the ability of singers to

open the mouth or to move the jaw. A computer (Macintosh

IIci, Apple Computer, CA) synthesizes the broadband signal as

a sum of sine waves with frequencies spaced at 5.38 Hz and

phases adjusted to improve the signal to noise ratio (Smith,

1995). During an initial calibration procedure, the microphone

measures pclosed, the pressure spectrum in response to the

broadband current with the mouth closed. Subsequently the

microphone measures popen, the spectrum of the response with

the mouth open and in parallel with the radiation impedance at

the mouth, and the ratio c is calculated, where c is given by

c ¼ popen=pclosed: (1)

Because the broadband source is a good approximation to a

current source, c is effectively equal to the ratio of the impedance

of the tract at the mouth, in parallel with the radiation field, to

that of the radiation field alone. The resonance frequencies were

manually detected from the recorded data by one author and

checked by another. In some measurements, particularly for

closed vowels, the impedance of the radiation field dominates

the measurements to such an extent that the tract resonances can-

not be unequivocally and precisely identified. This occurred in

16% of the 1374 measurements of R1, and in 6% of the meas-

urements of R2. In these cases that particular datum was disre-

garded. The error in resonance detection is typically 611 Hz.

B. The subjects

Twenty-two subjects volunteered to take part. Their ex-

perience varied from nationally recognized to amateur sing-

ers. Their range and experience are given in Table I. All but

four described their singing style as Western classical,

although some had had experience in other styles. The other

styles were jazz (singer B3) and musical theatre (singers S3,

T3). Singer T7 had no defined style. Baritones were used

rather than basses because Fig. 1(d) indicates that deliberate

resonance tuning would be very difficult to detect at very low

pitch. Sopranos had been studied earlier in our laboratory

(Joliveau et al., 2004a,b). However, in that study the singers

had been asked to sing softly, because of limited power in the

injected sound signal. The apparatus used here had higher

power so it was judged worthwhile to conduct new measure-

ments on the soprano range at a louder singing level.

C. The protocol

This study used the same set of four vowels as an earlier

study (Joliveau et al., 2004a,b), which had been chosen to

ensure ease of singing and measurement, sampling of the

phoneme space, and the effects of lip rounding. Each word

TABLE I. Details of the experimental subjects. Experience is specified using the taxonomy of Bunch and

Chapman (2000): 3 ¼ national/big city, 4 ¼ regional/touring, 5 ¼ local community (often semi-professional),

7 ¼ full-time voice student, 8 ¼ amateur (sings for pleasure). The lowest and highest pitches lie within the com-

fortable range of each singer.

Baritones Tenors

Singer B1 B2 B3 B4 T1 T2 T3 T4 T5 T6 T7 T8

Taxonomy 7 5 3 8 4 3 4 8 3 3 8 5

Lowest pitch G2 G2 A2 F2 G2 A2 C3 C3 C3 F2 C3 A2

Highest pitch F4 F4 D4 A4 A4 A4 C5 C5 B4 D5 G4 A4

Altos Sopranos

Singer A1 A2 A3 A4 S1 S2 S3 S4 S5 S6

Taxonomy 8 8 8 8 3 8 4 8 8 7

Lowest pitch E3 G3 F3 D3 G3 G3 G3 B3 G3 C4

Highest pitch G5 D5 E5 C5 D6 B5 A5 C6 B5 G6

1026 J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types

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to be sung was presented in writing on a card using the form

h<vowel>d, i.e., hard, hoard, who’d, and heard.

Subjects were asked to sing each note, at a comfortable

level and with as little vibrato as possible, in their trained

singing style, at a pitch that was indicated by a glockenspiel.

For each vowel, each note was presented in an ascending

scale, starting at the lowest note of what each singer identi-

fied as the comfortable range of his or her singing voice and

continuing to the highest note in the comfortable range. For

each vowel, after each scale had been completed, the sub-

jects were asked twice to repeat two or more of the notes in

the comfortable range at a similar loudness. This was to

allow an estimate of the reproducibility. Following this task,

they were asked to speak the carrier word rather than sing it.

For each token, the broadband signal was started after

the singer had begun a note and they were instructed to

continue for a second or so after it finished. Thus, for each

token, the recording included a sample of voice alone, voice

plus broadband signal followed by voice alone.

III. RESULTS AND DISCUSSION

A. The measured vocal tract resonances

1. The resonances of speech

Table II shows that the average measured values of R1

and R2 for speech were lower for altos than for sopranos in

all cases, except for R2 in “who’d.” However, in our small

sample only the values for R1 in “heard” and “hoard” and

R2 in “hard” and “hoard” differed significantly at the 5%

level between altos and sopranos. There were no statistically

significant differences between the resonances of tenors and

baritones. Thus in our sample, the voice range classifications

of alto and soprano, and tenor and baritone, were not corre-

lated with their values of R1 and R2 for speech. This differs

from the results of Cleveland (1977) where a correlation was

found between the resonance frequencies of speech and the

voice range classification of male singers. Although possibly

complicated by resonance tuning, the similarity between R1

and R2 of baritones and tenors was also evident during sing-

ing. The differences calculated using a total of 1277 meas-

urements for the 51 combinations of vowel and pitch where

measurements were made for both tenors and baritones were

–25 6 50 Hz for R1 and 15 6 90 Hz for R2.

2. The resonances during singing

Rather than keeping the resonances at the values used

for speech, all singers were found to vary their values of R1

and R2 as the fundamental frequency f0 varied while singing.

The reproducibility of the resonance measurements on indi-

vidual singers was tested by measuring a number of resonan-

ces three times at the same pitch whenever possible—see

Table III. At low pitches (below B4), the standard deviations

in R1 and R2, expressed as percentage, were similar for sing-

ing and speech across all singers. However at high pitches

(B4 and above) the proportional variation in R1 was typi-

cally reduced by around 50%. This is presumably because at

high pitch, singers then have a definite optimum value for

each resonance, particularly during resonance tuning,

whereas for speech the values of R1 and R2 need only fall in

the expected range for the desired vowel.

A similar effect was found when the variations among

singers were examined. Table IV shows that, again, the vari-

ation in R1 was reduced considerably for altos and sopranos

when f0 exceeded R1o, defined as the value of R1 in speech.

Otherwise, the variations between singers in different ranges

appear not to be significant. Figure 2 shows the combined

data for altos and sopranos when singing the vowels in

“hard” and “who’d.” The large reduction in variability at

high pitch provides strong evidence that deliberate resonance

TABLE II. The measured resonance frequencies for speech for the singers

in different vocal ranges.

Vowel

Voice Hard Heard Hoard Who’d

R1o (Hz)

Soprano 825 6 120 610 6 50 585 6 45 410 6 80

Alto 830 6 95 540 6 20 515 6 40 350 6 30

Female 825 6 110 580 6 50 555 6 55 390 6 70

Tenor 700 6 85 555 6 90 545 6 100 350 6 30

Baritone 785 6 120 520 6 65 495 6 85 385 6 85

Male 725 6 100 545 6 80 530 6 95 365 6 55

R2o (Hz)

Soprano 1340 6 115 1560 6 345 1065 6 90 1340 6 475

Alto 1160 6 60 1525 6 140 825 6 85 1510 6 280

Female 1265 6 130 1545 6 270 970 6 150 1410 6 400

Tenor 1175 6 85 1340 6 90 900 6 115 1145 6 245

Baritone 1235 6 50 1360 6 125 880 6 175 1205 6 335

Male 1190 6 80 1345 6 100 890 6 130 1165 6 265

TABLE III. The reproducibility of vocal tract configurations for individual

singers. Percentage deviations in Ri were calculated from measurements

repeated at the same pitch for each vowel and singer. The standard deviation

rRi was then calculated from these data across all singers in a given fre-

quency range and finally expressed as a percentage. The numbers in brackets

indicate the number of measurements. �Because no repetitions were made

for speech in this study, the standard deviations presented for speech were

calculated from a separate study on 11 female speakers performed using the

same apparatus in the same laboratory (Swerdlin et al., 2010).

Vowel

Hard Heard Hoard Who’d All vowels

rR1 (%)

Female speech� 7.8 (41) 6.8 (52) 6.0 (55) 9.4 (50) 7.1 (251)

Female singing

(below B4)

6.6 (29) 8.0 (34) 6.8 (38) 5.8 (27) 6.8 (128)

Female singing

(above B4)

3.3 (11) 5.7 (9) 2.7 (6) 2.0 (14) 3.4 (40)

Male singing 5.6 (68) 4.5 (83) 5.5 (75) 6.4 (69) 5.5 (295)

rR2 (%)

Female speech� 2.0 (53) 4.7 (54) 3.4 (55) 6.1 (53) 4.5 (267)

Female singing

(below B4)

2.6 (42) 3.6 (38) 6.0 (38) 5.5 (38) 4.6 (156)

Female singing

(above B4)

1.1 (15) 2.3 (12) 2.9 (11) 9.6 (14) 5.2 (52)

Male singing 3.8 (76) 6.5 (86) 3.7 (90) 5.5 (74) 5.0 (326)

J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types 1027

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tuning is occurring. There are several different possibilities

for resonance tuning at low pitch (see Fig. 1), and in this

range resonance tuning might even increase the variation

among singers if different singers tune the resonances to dif-

ferent harmonics.

3. The effect of resonance tuning

Figure 3 shows examples of the measured pressure ratio

c during singing. In each case the fundamental of the sung

pitch f0 and its harmonics are visible as spikes superimposed

over the measured broadband spectrum. Resonances in the

vocal tract are associated with maxima in the broadband

response. Figure 3(a) shows an example where R1, R2, f0,

and 2f0 all occur at different frequencies, indicating that, in

this case, there was no adjustment of resonances to harmon-

ics. Consequently these resonances make only a modest dif-

ference to the spectral envelope of the voice. Figure 3(b)

shows an example where R1 coincides with 2f0 and R2 coin-

cides with 5f0 (R1:2f0 and R2:5f0 tuning, respectively). As a

result, the second harmonic now has greater energy than the

first harmonic, and the fifth harmonic has greater energy

than the fourth, as indicated by their higher spikes.

When the frequency of a resonance is determined by the

pitch of the note sung, instead of or as well as by the vowel

sung, vowel quality may be affected. For sopranos, the

impact on vowel intelligibility can be quite significant (e.g.,

Scotto di Carlo and Germain, 1985; Benolken and Swanson,

1990) as can be clearly demonstrated with appropriate sound

examples (Music Acoustics, 2010). In the present study,

altos, tenors, and baritones usually adjust R1 over a smaller

range that do sopranos, so the effects on intelligibility might

be less important as the adjustments are often smaller than

the characteristic separation in the vowel plane at which

vowels become confused (Dowd et al., 1998). Although

these resonance-tuning strategies can surely impact per-

ceived vowel quality, they were not studied here.

B. What constitutes “resonance tuning?”

A production of any given vowel in speech will be char-

acterized by particular values of R1 and R2. Figure 1 shows

that, with the exception of the highest part of the soprano

range, there will always be at least one value of the funda-

mental frequency f0, where f0 or one of its harmonics

matches R1. A similar situation occurs for R2. If R1 and R2

were held at constant values throughout the vocal range of a

TABLE IV. The variation in vocal tract resonances among different singers.

The standard deviations in Ri, rRi, were calculated from measurements at

the same pitch for each vowel and singer. Equivalent values for speech are

given in Table II.

Vowel

Hard Heard Hoard Who’d

rR1 (Hz)

Female ( f0 � Rio) 145 85 105 50

Female ( f0 > Rio) 35 35 40 25

Male 105 90 75 65

rR2 (Hz)

Female 135 155 125 200

Male 115 95 120 195

FIG. 2. The variation in resonance frequency R1 among the ten female sing-

ers (altos þ sopranos) as a function of frequency on a log–log scale. The

dashed diagonal line indicates the relationship R1 ¼ f0. The error bars indi-

cate the standard deviations; they are too small to be shown for several

points close to or on the diagonal line indicating R1:f0 tuning. The gray

shaded areas indicate the range of 6standard deviation of R1o measured for

these vowels and singers during speech.

FIG. 3. The effect of matching a resonance with a harmonic for alto A1

singing the vowel in “heard” at two different pitches, mezzoforte. The quasi-

continuous line shows the measured pressure ratio c (¼ popen=pclosed) as a

function of frequency; maxima in this curve indicate the resonance frequen-

cies. The sharp peaks superposed on the curve are the harmonics of her

voice. In the figure on the left she sings at pitch B3 (247 Hz) and none of the

low harmonics fall very close to the resonances. In the figure on the right

she sings at pitch D4 (294 Hz) and, for this note, the second and fifth har-

monics fall close to the first two resonances.

FIG. 4. An example of simultaneous R1:f0 and R2:2f0 tunings by soprano

S5 on the vowel in “heard” shown in a log–log plot. The horizontal lines

indicate the values of R1 and R2 measured for this singer and vowel in

speech. The dashed diagonal lines indicate the relationships Ri ¼ nf0.

1028 J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types

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singer, these isolated matches would produce sudden

increases in the sound level and changes in timbre as the

singer sang a chromatic scale, passing f0 through R1 and R2.

This study is concerned with determining when resonance

tuning occurs; this involves a singer adjusting the resonance

frequencies to help match resonances to f0 or a harmonic.

For the high part of the normal soprano range, only one

strategy is effectively available for each resonance—resonance

tuning is then “systematic” and would be expected to occur over

a substantial pitch range. Figure 4 shows two examples of such

systematic resonance tuning where the same strategy is em-

ployed over a range of pitch; they are R1:f0 and R2:2f0 tuning.

For lower pitch ranges, the number of possibilities

increases—see Fig. 1. It might therefore be expected that several

different strategies for resonance tuning would be employed

within a given lower voice range. Each might only occur at a

couple of notes, or perhaps even at a single pitch, in which cases

the term resonance tuning strategy would hardly be appropriate.

It is relatively easy to detect the presence of resonance

tuning in the high voice ranges because it is likely to be

FIG. 5. The matching between resonances and harmonics for different voice ranges, the numbers on the abscissa indicating different singers. The tail of each

arrow indicates the value of �Doi , the average absolute difference in frequency between the resonance Ri and the closest harmonic, if Ri were held constant at its

average value for that singer, vowel, and measured range. The tip of each arrow indicates �Di, the average absolute difference in frequency when the measured

values of Ri are taken into account. Thus a downward pointing arrow indicates improved matching between resonance and harmonic over the measured range.

A solid circle indicates that there was no significant difference between �Di and �Doi .

J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types 1029

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maintained over a significant range of pitch frequencies, and

the tuning becomes obvious as the resonance is shifted well

outside its normal range for that vowel in speech. The situa-

tion is more difficult for low-pitched voices because the reso-

nance can be tuned, but still remain within the normal

resonance range for that vowel. In order to quantify reliably

the extent of resonance tuning, a parameter Di is defined that

is equal to the absolute difference in frequency between the

ith resonance Ri and nf0, the harmonic closest to that reso-

nance. Thus,

Di ¼ jRið f0Þ � nf0j: (2)

�Di can then be defined as the average value of Di over a par-

ticular pitch range.

If no attempt were made to alter Ri and if it were main-

tained constant at a value denoted by Rio over the pitch range

of interest, this value of �Di can be defined as �Doi , i.e.,

�Doi ¼ the average absolute difference jRio � nf0j: (3)

Thus �Di < �Doi implies that the shifts of Ri with frequency are

helping with the overall matching of resonances with har-

monics. Figure 5 shows the values of �Doi (indicated by the

tail of each arrow) and �Di (indicated by the tip of each

arrow) calculated for each combination of singer and vowel

over their measured pitch range. The values of �Doi were cal-

culated using the average measured values of Ri over the

same range. Similar results were obtained using the values

of Rio measured for speech.

In the absence of any resonance tuning, one would expect

Fig. 5 to show about equal numbers of up- and down-pointing

arrows. It is immediately apparent that the variation of R1 with

pitch measured for most sopranos (the exception was S3) over

their pitch range dramatically reduced the average frequency

difference between R1 and the nearest harmonic. The match-

ing is closest for the vowel in “who’d,” which in speech has

the lowest value of R1 of those studied—see Table II. All

sopranos and altos showed significant matching over the meas-

ured voice range for this vowel. The situation was quite differ-

ent for baritones and tenors where significantly improved

matching was less common; indeed on occasions the differ-

ence �Doi � �D1 even changed sign indicating a larger average

difference in frequency between resonance and harmonic.

The matching was more varied for R2, with occasional

significant improvements in matching, but also many cases

where the matching became worse. It now remains to look at

each voice type in detail and to determine the particular reso-

nance strategies involved.

C. Resonance tuning in the soprano range

Figure 6 shows the ranges over which R1 was close to f0(R1:f0 tuning) and R2 was close to 2f0 (R2:2f0 tuning) for the

measured data on altos and sopranos.

It can be seen from Fig. 6 that all sopranos employed R1:f0tuning over some part of their range for every vowel studied.

Their measured value of R1 for speech was usually within, or

close to, this tuning range. Consequently the lower value of R1

FIG. 6. The frequency ranges for resonance tuning for female singers meas-

ured for four different vowels. For each singer the lower darker shaded box

indicates R1:f0 tuning and the upper lighter shaded box indicates R2:2f0 tun-

ing. The full and open circles indicate the value for R1 and R2/2, respec-

tively, measured for that singer for speech.

1030 J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types

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for “who’d” meant that R1:f0 tuning commenced at a lower

pitch for this vowel and extended over a greater range. This is

consistent with the results of Joliveau et al. (2004a,b).

Figure 6 also shows that most sopranos employ R2:2f0tuning over at least a small part of their range, and this often

occurs simultaneously with R1:f0 tuning (though not often for

the vowel in “hoard”). This is not surprising: the most com-

monly observed gesture that increases R1 is increasing mouth

opening. Although R2 depends primarily on tongue shape

and position, it also increases with increasing mouth opening.

Consequently, R2:2f0 tuning over part of the range of R1:f0tuning might require little extra adjustment. Figure 4 shows

an example of simultaneous R1:f0 and R2:2f0 tunings.

D. Resonance tuning in the alto range

Figure 7 shows examples of two different tuning strat-

egies used by altos. Alto A1 used systematic R1:f0 tuning

once f0 became comparable with the value of R1 measured

in speech. Alto A2 used R1:f0 tuning for the vowel with the

lowest value of R1 in speech but switched to R1:2f0 tuning

for the other vowels. This allowed resonance tuning to occur

at lower pitches than if R1:f0 tuning were used.

E. How closely are resonances tuned to one of theharmonics?

The values of �Di and �Doi presented in Fig. 5 were calcu-

lated over the complete measured range for each singer and

vowel. It is now interesting to examine how the resonance

frequencies are distributed around the nearest harmonic.

Accordingly Fig. 8 presents histograms of the frequency dif-

ference R1 – f0 (i.e., D1). Figure 8(a) presents the combined

data for all the combinations of soprano and vowel measured

in this study. A broad peak that is approximately 20 Hz wide

and centred upon R1 ¼ f0 is apparent. Figure 8(b) presents

the combined data for all the combinations of soprano and

vowel measured in this laboratory: Six from this study, nine

from Joliveau et al. (2004b) and 12 from Garnier et al.(2010), and a narrower peak when R1 ¼ f0 is now visible.

FIG. 7. Examples of two different tuning strategies used by altos. Alto A1 used systematic R1:f0 tuning once f0 approached the value of R1 measured in

speech. Alto A2 used R1:f0 tuning for the vowel with the lowest value of R1 in speech, but switched to R1:2f0 tuning for the other vowels. The horizontal lines

indicate the values of R1 measured for that singer and vowel in speech. In two cases (A1-who’d and A2-hard) measurements for speech were not available and

consequently the average values for the other altos were used. The dashed diagonal lines indicate the relationships Ri ¼ nf0. The standard deviations in R1 cal-

culated across all vowels from measurements repeated at the same pitch were 62.1% and 67.7% for A1 and A2, respectively.

FIG. 8. Histograms showing the distribution of

the measured values of R1 about f0. (a) presents

the combined data for all the 190 combinations

of soprano and vowel measured in this study.

(b) presents the combined data for all the 511

combinations of soprano and vowel measured

in this laboratory; six sopranos and four vowels

from this study, nine sopranos and four vowels

from Joliveau et al. (2004b) and 12 sopranos

and one vowel from Garnier et al. (2010).

J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types 1031

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These histograms suggest that, within the resolution of our

measurements, sopranos appear to tune R1 � f0, rather than

just tuning R1 > f0.

Table V presents the values of �Di for the individual sopra-

nos and altos calculated only for the measurements where res-

onance tuning was apparent. The histograms for D1 (Fig. 8)

and D2 indicate that, at least for these experiments, resonance

tuning could be assumed when Di < 25 Hz. Table V indicates

that the average difference �D1 during resonance tuning is

around 9 Hz; this is similar to the resolution of our technique

for measuring tract resonances. The average value of �D2 was

around 12 Hz.

One important consideration is whether Ri is tuned

higher or lower in frequency than the nearest harmonic, as

this will make the acoustic load on the vocal folds caused by

the vocal tract to be inertive or compliant, respectively.

FIG. 9. The proximity of the resonances R1 and R2 to the nth harmonic of the sung pitch f0. The numbers in the figure indicate the value of n for the harmonic

that was nearest to the resonance, provided the frequency difference �Di was <50 Hz. A dot indicates the measurement where the frequency difference between

harmonic and resonance exceeded 50 Hz. Harmonics greater than the ninth are indicated using the notation; a ¼ 10, b ¼ 11, c ¼ 12, d ¼ 13, e ¼ 14, f ¼ 15,

and g ¼ 16.

1032 J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types

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Models suggest that this has implications for the amplitude

and stability of vocal fold vibration (Titze, 1988; Fletcher,

1993). To investigate this, the following three new variables

are introduced,

�di ¼ the average signed difference ðRið f0Þ � nf0Þ (4)

mþ ¼ number of measurements in which ðRið f0Þ> nf0Þ (5)

m� ¼ number of measurements in which ðRiðf0Þ< nf0Þ (6)

where n denotes the nearest harmonic. Table V shows that

the values for �d1 tend to be slightly negative, suggesting that

R1( f0) < nf0 for most singers. This is also supported by the

ratio mþ/m� which was usually �1. However, for R2 the ra-

tio mþ/m� was typically around 1, indicating that R2 was

equally likely to be above or below 2f0 in frequency. The

exception was S6, where the values of �d1 and �d2 indicate that

R1 was tuned around 10 Hz above f0, and R2 was tuned

around 11 Hz above 2f0, for almost all measurements. It

should be remembered that these measured values of the dif-

ferences �Di and �di are of the same order as the resolution of

our technique, and it would only require a small systematic

error in our estimates of the resonance frequencies to skew

their distribution about the closest harmonic.

F. Resonance tuning by tenors and baritones

Although Fig. 1 illustrates that many possible tuning

strategies exist for the lower pitched voice, Fig. 5 indicates

that significant improvements in matching resonances to har-

monics are much less common than for the higher pitched

voices. To help identify tuning strategies, and also to provide

comparison with the strategies used at higher pitch, Fig. 9

shows the nearest harmonic to each Ri provided that Di < 50

Hz. Thus the numeral 1 appearing in the R1 region of the fig-

ure indicates that R1:f0 tuning within 50 Hz was evident at

this pitch for this singer and vowel, and a numeral 3 in the

R2 region would indicate R2:3f0 tuning at that pitch.

Figure 1 shows that the R1:f0 tuning used by all sopra-

nos, and some altos, is possible for the higher range of the

tenor and baritone voice. However Fig. 9 shows that it was

only used sparingly by one tenor in our sample, with the

greatest range being for the vowel with the lowest value of

R1 in speech (who’d)—see Fig. 10.

Figure 1 indicates that R1:2f0 and R1:3f0 tunings are possi-

ble in the range below about C5, and most of the singers used

these tunings, even if for only a small part of their range—see

Fig. 10. Figure 10 also provides an example where tenor T1

successively exhibited R1:4f0, R1:3f0 and R1:2f0 tunings once

the appropriate harmonic approached the value of R1 in speech

as the pitch increased. Tunings such as shown in Fig. 10 can-

not be maintained over a wide pitch range because the value

TABLE V. The average frequency differences between resonance Ri and

the closest harmonic for altos and sopranos calculated over the regions

where R1:f0 and R2:2f0 tunings occurred. The symbol �Di indicates the aver-

age absolute difference and �di indicates the average signed difference from

the nth harmonic. The number of measurements for which Ri � nf0 and

Ri < nf0 are indicated by mþ and m�, respectively.

Singer

R1:f0 tuning R2:2f0 tuning

�D1 (Hz) �d1 (Hz) mþ/m� �D2 (Hz) �d2 (Hz) mþ/m�

S1 9 2 6/8 11 �6 2/6

S2 8 �1 8/11 11 �3 2/2

S3 9 �4 3/3 10 3 3/3

S4 12 �4 10/13 11 8 5/2

S5 9 �5 6/14 10 0 2/3

S6 11 10 17/2 13 11 6/1

A1 9 �6 6/16 13 0 2/5

A3 9 �6 2/7 — — —

All 9 �2 60/80 12 4 23/22

FIG. 10. An example showing some different

tunings of R1 used by tenors. Tenor T6 is

seen to use R1:f0 tuning once the pitch

approaches the value of R1 in speech. Tenor

T1 used R1:2f0 tuning once 2f0 approached

the value of R1 in speech. For the vowel in

“heard,” T1 also exhibited R1:3f0 and R1:4f0tunings when the relevant harmonic

approached the value of R1 in speech. The

horizontal lines indicate the values of R1

measured for speech for that singer and

vowel. The standard deviations in R1 calcu-

lated from measurements repeated at the

same pitch for the vowels shown were

64.0% and 63.5% for T1 and T6,

respectively.

J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types 1033

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of R1 rapidly approaches the upper limit of its range. Tenors

often exhibited R1 within 50 Hz of harmonics above the

fourth, although only for one or two notes. Figure 11 shows an

example of R1:2f0 tuning by baritone B3. Figure 11 also shows

an interesting example where baritone B2 increases R1 sys-

tematically with increasing pitch, but maintains R1 just above

f0 so R1 � 1.15 f0. One possible explanation is that the band-

width of R1 in this case was such that these values of D1 might

still produce a useful increase in volume.

For some singers and vowels there appeared also to be

deliberate tuning of R2. Figure 12 shows how, as the pitch

increases, baritone B1 successively uses R2:5f0, R2:4f0, and

R2:3f0 tunings.

G. Consequences for singing synthesis-by-rule

These measurements have some implications for synthe-

sis-by-rule singing systems. One main observation is that R1

should not be kept constant at the value for speech, but

should be varied with pitch, even in cases where there is no

tuning of resonances to harmonics. It presumably reflects the

adjustments in articulation that commonly accompany a

pitch rise, such as mouth opening, jaw lowering, and larynx

rise. The systematic R1:f0 tuning observed for female sing-

ers, when the pitch approaches the normal range of R1,

should be implemented as a main rule. The tuning of R1 to

2f0 or higher harmonics could be implemented as an addi-

tional, but not compulsory, rule. Its perceptual effect on

timbre lies beyond the scope of the present study, but has been

mentioned in previous works (Boersma and Kovacic, 2006;

Henrich et al., 2007). The R2:2f0 tuning observed here, and

also reported by Garnier et al. (2010), could also be imple-

mented as a possible rule in the top range of soprano voice.

IV. CONCLUSIONS

This study confirms and extends the occurrence of R1:f0tuning by sopranos in the higher part of their range. All of

the 27 sopranos studied in this laboratory [six in this study,

nine in Joliveau et al. (2004b) and 12 in Garnier et al.(2010)] have shown R1:f0 tuning over at least part of their

upper range—a total of 72 separate singer/vowel combina-

tions. Such consistency might encourage composers and

librettists to consider matching vowel to pitch when writing

for the soprano voice (Smith and Wolfe, 2009).

Most sopranos employed R2:2f0 tuning over at least a

part of their range, and this often occurred simultaneously

with R1:f0 tuning.

Altos use R1:f0 tuning for the vowels with lower values

of R1 in speech. They may switch to R1:2f0 tuning in lower

part of their range.

Tenors and baritones generally used R1:2f0 and R1:3f0tunings over at least part of their range. A number of differ-

ent tunings to higher harmonics occurred at lower pitch.

Occasionally a detailed resonance tuning of R2 occurred.

The implications for singing synthesis are that R1:f0 tun-

ing should be implemented for sopranos as a necessary rule,

and that the tuning of R1 to 2f0 or higher harmonics could be

implemented as an additional, but not compulsory, rule.

The results indicate that singers can repeatedly tune

their resonances with a precision of typically 20 Hz.

There can be considerable differences in the resonance

strategies used by singers, particularly for voices in the lower

ranges. Care should consequently be taken in extrapolating

results from a single subject.

ACKNOWLEDGMENTS

We warmly thank our volunteer subjects for their patience

and availability. We thank the Australian Research Council for

support and Maeva Garnier for helpful discussions.

1In acoustics, the word “formant” is variously used to describe a broad

peak in the spectral envelope, the acoustic resonance in a system that gives

rise to it, or a property of a filter used to model the system. To avoid possi-

ble confusion “formant” is not used in this paper.

FIG. 11. An example showing different tun-

ings of R1 used by baritones for the vowel

in “who’d.” Baritone B3 is seen to use

R1:2f0 tuning once the pitch exceeds G3 ( f0� 200 Hz). Baritone B2 provides a rare

example where R1 is consistently and

clearly tuned above f0. The horizontal lines

indicate the values of R1 measured for

speech for that singer and vowel. The stand-

ard deviations in R1 calculated from

repeated measurements repeated at the same

pitch for the vowel in “who’d” were 63.5%

and 69.0% for B2 and B3, respectively.

FIG. 12. An example showing three different tunings of R2 used by baritone

B1 for the vowel in “who’d.” As the pitch increases the singer successively

uses R2:5f0, R2:4f0, and R2:3f0 tuning. The horizontal line indicates the

value of R2 measured for speech for this singer. The standard deviation in

R2 calculated from repeated measurements repeated at the same pitch for

this singer and vowel was 61.1%.

1034 J. Acoust. Soc. Am., Vol. 129, No. 2, February 2011 Henrich et al.: Resonance tuning by different voice types

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